Simulating large time-to-event trials in NONMEM
Joakim Nyberg, Kristin E. Karlsson, Siv Jönsson, Ulrika S.H. Simonsson, Mats O. Karlsson and Andrew C. Hooker
Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Simulation of clinical trials is useful in e.g. model based power calculations, visual diagnostics during model building, predicting clinical trials and decision making. Simulating large time-to-event (TTE) trials is in NONMEM (NM) [1] traditionally performed using a dense grid dataset and utilizing the cumulative hazard to predict if an event occurred between two grid points [2, 3]. However, this method becomes impractical if the number of subjects is high, study is long and/or frequent grid points are needed, resulting in that a simulation data set may exceed 1 GB.
The objective of this work was to develop methods to perform TTE trial simulations in NM with precision in the simulations similar to dense grid simulations, but without huge input data sets.
Methods: With the developed method, using the original data set, the NM code simulates event times and based on these a table output with the resulting dependent variable at the event time is generated similar to the output obtained with dense grid data set simulation. The method was implemented for 4 parametric TTE distributions/survival functions: Exponential (E), Weibull (W), Gompertz (G), Log-Normal (LN), with covariate effects included proportional to the baseline hazard.
Two scenarios were investigated; S1) time independent covariates and S2) time dependent covariates, for a large data set (3 year study with ~14000 patients).
In S1, the event time was obtained using analytic solutions of the survival functions [4]. In S2, the survival function could not be solved analytically and event times was obtained using $DES with T and MTIME to assure that the implicit event grid was good enough for the acquired precision in the simulations.
Results: With S1, the study was simulated 100 times within 10 minutes with a total event data set size of ~65MB with a maximal precision (analytic). With time dependent covariates (S2) using at least a 1 day event precision (MTIME=0.5 days) 100 trials were simulated in less than 1 hour with a total event data set size of ~65MB compared to the grid solution of 1 day precision which had an input data set > 3 GB and could not be run with NM.
Conclusions: Efficient TTE trial simulations were implemented in NM without losing precision in the event time simulations. The technique is general and could easily be adapted to repeated TTE and to other models than those investigated. The precision for the S2 scenario could be further increased by decreasing the MTIME.
Acknowledgement: This work was part of the DDMoRe project.
References:
[1] Beal, S., Sheiner, L.B., Boeckmann, A., & Bauer, R.J., NONMEM User's Guides. Introduction to NONMEM 7. Icon Development Solutions (2014).
[2] Holford N & Lavielle M. Time-to-event tutorial. 2011 http://www.page-meeting.org/default.asp?abstract=2281
[3] Holford N. Time To Event Analysis. Diagnostic plots. http://holford.fmhs.auckland.ac.nz/docs/time-to-event-diagnostics.pdf
[4] Bender R, Augustin T. and Blettner M. Generating survival times to simulate Cox proportional hazards models. Statist. Med. 2005; 24:1713–1723.
